Free Grade 3 Introducing Scalar Multiples Common Errors Lessons
Free Grade 3 lessons for Introducing Scalar Multiples Common Errors: 12 real questions with a full answer key and worked solutions. Factors divide a number exactly; multiples are in its times table. The HCF is the biggest shared factor, the LCM the smallest shared multiple.
Free
Core
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing scalar multiples common errors
Explain introducing scalar multiples common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing scalar multiples common errors
Calculate introducing scalar multiples common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing scalar multiples common errors
Compare introducing scalar multiples common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing scalar multiples common errors
Justify introducing scalar multiples common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Introducing Scalar Multiples Common Errors works
Factors divide a number exactly; multiples are in its times table. The HCF is the biggest shared factor, the LCM the smallest shared multiple.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.List all the factors of 12.[1]
- 2.List all the factors of 20.[1]
- 3.List all the factors of 30.[1]
- 4.List all the factors of 36.[1]
- 5.Find the highest common factor (HCF) of 42 and 30.[2]
- 6.Find the highest common factor (HCF) of 35 and 14.[2]
- 7.Find the highest common factor (HCF) of 49 and 49.[2]
- 8.Find the highest common factor (HCF) of 15 and 35.[2]
- 9.Find the lowest common multiple (LCM) of 56 and 32.[3]
- 10.Find the highest common factor (HCF) of 42 and 42.[3]
- 11.Find the lowest common multiple (LCM) of 10 and 14.[3]
- 12.Find the lowest common multiple (LCM) of 15 and 35.[3]
Show answers and working
1. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
2. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
3. 1, 2, 3, 5, 6, 10, 15, 30
Find factor pairs that multiply to 30. 1 × 30 2 × 15 3 × 10 5 × 6
4. 1, 2, 3, 4, 6, 9, 12, 18, 36
Find factor pairs that multiply to 36. 1 × 36 2 × 18 3 × 12 4 × 9 6 × 6
5. 6
List factors of 42 and 30. The largest factor they share is 6.
6. 7
List factors of 35 and 14. The largest factor they share is 7.
7. 49
List factors of 49 and 49. The largest factor they share is 49.
8. 5
List factors of 15 and 35. The largest factor they share is 5.
9. 224
HCF(56, 32) = 8. LCM = 56 × 32 ÷ 8 = 224.
10. 42
List factors of 42 and 42. The largest factor they share is 42.
11. 70
HCF(10, 14) = 2. LCM = 10 × 14 ÷ 2 = 70.
12. 105
HCF(15, 35) = 5. LCM = 15 × 35 ÷ 5 = 105.
Worked examples
List all the factors of 24.
- Find factor pairs that multiply to 24.
- 1 × 24
- 2 × 12
- 3 × 8
- 4 × 6
- Answer: 1, 2, 3, 4, 6, 8, 12, 24
Find the highest common factor (HCF) of 45 and 36.
- List factors of 45 and 36.
- The largest factor they share is 9.
- Answer: 9
Find the lowest common multiple (LCM) of 27 and 18.
- HCF(27, 18) = 9.
- LCM = 27 × 18 ÷ 9 = 54.
- Answer: 54
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Mixes up factors and multiples.
Correction: Factors are Few (they fit inside), multiples are Many (they go on forever).
Misses factor pairs.
Correction: Work through 1, 2, 3… in order until the pairs meet.
Teacher tips
- · Use factor rainbows to show pairs.
Parent tips
- · Ask how many ways 24 sweets can be put into equal bags.
Real-life applications
- · Arranging chairs in equal rows, syncing bus timetables (LCM).
Assessment objectives
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Frequently asked
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- What should a learner already know before this?
- Start with Introducing Scalar Multiples Word Problems, Introducing Scalar Multiples Techniques, Adding Vectors. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Introducing Scalar Multiples Common Errors?
- Move on to Working with Scalar Multiples, Scalar Multiples in Context, which build directly on this idea.
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